extreme f(x)= x/(x^2-x+2)

Lösung

extrempunkte

f (x) = \frac{x}{x ^{2} - x + 2}

Minimum (- 2, - \frac{2 2 - 1}{7}), Maximum (2, \frac{2 2 + 1}{7})

Schritte zur Lösung

f^{'} (x) = \frac{- x ^{2} + 2}{( x ^{2} - x + 2 ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = - 2

\frac{x}{x ^{2} - x + 2} : - \frac{2 2 - 1}{7}

Minimum (- 2, - \frac{2 2 - 1}{7})

Stecke

x = 2

\frac{x}{x ^{2} - x + 2} : \frac{2 2 + 1}{7}

Maximum (2, \frac{2 2 + 1}{7})

Minimum (- 2, - \frac{2 2 - 1}{7}), Maximum (2, \frac{2 2 + 1}{7})

e x t re m e f (x) = 7 x - 28 x

e x t re m e f (x) = ((x y) - λ (6 x + y - 20))

e x t re m e y = \frac{x + 3}{2}

e x t re m e f (x, y) = 3 x^{2} - x y + y^{2} - 11 x

e x t re m e f (x, y) = (x - 1)^{2} - (y - 1)^{2}